Impact of Joule heating and viscous dissipation on magnetohydrodynamics boundary layer flow of viscous nanofluid subject to the stretched surface

2021 ◽  
pp. 095440892110641
Author(s):  
M. Riaz Khan ◽  
Awatef Abidi ◽  
Jamel Madiouli ◽  
Kamel Guedri ◽  
A.M. Al-Bugami ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Base Fluid ◽  
Fluid Temperature ◽  
Suction Parameter ◽  
Nanoparticles Concentration ◽  
The Impact

The two-dimensional magnetohydrodynamics incompressible flow of nanofluid about a stretching surface is investigated with the existence of viscous dissipation and Joule heating. Moreover, the impact of the convective condition and mass suction is applied with the viscous nanofluid containing copper nanoparticles and the base fluid water. The similarity variables have been employed to transform the coupled nonlinear partial differential equations into the ordinary differential equations and the numerical scheme bp4c is implemented for the further analysis of the solution. The diverse results of temperature, skin friction coefficient, velocity, and the Nusselt number according to numerous parameters have been shown graphically. It appears that the Nusselt number and the skin friction reduces, which is caused by the enhancement of both Hartman number and nanoparticles concentration. Moreover, the fluid temperature surges with the growth of Biot number, and Eckert number whereas the growth of nanoparticles concentration and suction parameter diminishes the velocity and temperature profile. The inclusion of a significant quantity of nanoparticles in the base fluid increases the density of the corresponding nanofluids and accordingly the temperature of the coupled nanoparticles in the base fluids can be modified. Hence, nanofluids build an outstanding performance in electronic components appliances and other electrical devices. The existing research is further effective in refrigerators for stabilizing their rate of cooling.

scholarly journals EFFECT OF HEAT AND MASS TRANSFER AND THERMAL RADIATION ON A STEADY MHD CONVECTIVE FLOW WITH VISCOUS DISSIPATION AND SUCTION/INJECTION

2022 ◽  
Vol 52 (1) ◽  
pp. 35-41
Author(s):  
Silpisikha Goswami ◽  
Kamalesh Kumar Pandit ◽  
Dipak Sarma
Keyword(s):  
Nusselt Number ◽  
Thermal Radiation ◽  
Temperature Profile ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Sherwood Number ◽  
Fluid Velocity ◽  
Physical Parameters ◽  
Flow Equations ◽  
The Impact

Our motive is to examine the impact of thermal radiation and suction or injection with viscous dissipation on an MHD boundary layer flow past a vertical porous stretched sheet immersed in a porous medium. The set of the flow equations is converted into a set of non-linear ordinary differential equations by using similarity transformation. We use Runge Kutta method and shooting technique in MATLAB Package to solve the set of equations. The impact of non-dimensional physical parameters on flow profiles is analysed and depicted in graphs. We observe the influence of non-dimensional physical quantities on the Nusselt number, the Sherwood number, and skin friction and presented in tables. A comparison of the obtained numerical results with existing results in a limiting sense is also presented. We enhance radiation to observe the deceleration of fluid velocity and temperature profile for both suction and injection. While enhancing porosity parameter accelerates velocity whereas decelerates temperature profile. As the heat source parameter increases, the temperature of the fluid decreases for both suction and injection, it has been found. With the increasing values of the radiation parameter, the skin friction and heat transfer rate decreases. Increasing magnetic parameter decelerates the skin friction, Nusselt number, and Sherwood number.

scholarly journals Magnetohydrodynamic Hybrid Nanofluid Flow Past an Exponentially Stretching Sheet with Slip Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3291
Author(s):  
Abdul Samad Khan ◽  
He-Yong Xu ◽  
Waris Khan
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Slip Parameter ◽  
Nanofluid Flow ◽  
Slip Conditions ◽  
Exponentially Stretching ◽  
The Impact

This study presents the magnetized hybrid nanofluid flow with heat source/sink over an exponentially stretching/shrinking sheet. Slip conditions are implemented to analyze the hybrid nanofluid flow for both slip and no-slip conditions. Additionally, the hybrid nanofluid of alumina and copper (hybrid nanoparticles) with blood (base fluid) has been considered and discussed with both suction and injection parameters. The appropriate similarity variables are used to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and solved analytically with the help of the homotopy analysis method (HAM). The impact of different embedded parameters has been shown in the form of graphs and tables. The numerical values of skin friction and Nusselt number are presented in the form of Tables for both slip and no-slip cases. It is summarized that the upsurge of the velocity slip parameter and magnetic parameter increases the skin friction, while the rising of the thermal slip parameter and heat generation parameter decreases the Nusselt number.

Effects of Viscous Dissipation and Joule Heating on Natural Convection Flow of a Viscous Fluid from Heated Vertical Wavy Surface

2011 ◽  
Vol 66 (6-7) ◽  
pp. 427-440 ◽  
Author(s):  
Nasser S. Elgazery ◽  
Nader Y. Abd Elazem
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Wavy Surface ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Local Skin ◽  
Local Skin Friction

A mathematical model will be analyzed in order to study the effects of viscous dissipation and Ohmic heating (Joule heating) on magnetohydrodynamic (MHD) natural convection flow of a temperature dependent viscosity from heated vertical wavy surface. The present physical problem is studied numerically by using the appropriate variables, which reduce the complex wavy surface into a flat one. An implicit marching Chebyshev collocation scheme is employed for the analysis. Numerical solutions are obtained for velocity, temperature, local skin friction, and Nusselt number for a selection of parameter sets consisting of Eckert number, Prandtl number, MHD variation, and amplitude-wavelength ratio parameter. Numerical results show that these parameters have significant influences on the velocity and the temperature profiles as well as for the local skin friction and Nusselt number

scholarly journals Numerical and Analytical Investigation for Darcy-Forchheimer Flow of a Williamson Fluid over a Riga Plate with Double Stratification and Cattaneo-Christov Dual Flux

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
S. Eswaramoorthi ◽  
Nazek Alessa ◽  
M. Sangeethavaanee ◽  
Ngawang Namgyel
Keyword(s):  
Nusselt Number ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Viscous Fluids ◽  
Fluid Temperature ◽  
Williamson Fluid ◽  
Injection Parameter ◽  
Riga Plate ◽  
The Impact ◽  
Forchheimer Flow

The Darcy-Forchheimer flow of a Williamson fluid over a Riga plate was analyzed in this paper. Energy and mass equations are modeled with Cattaneo-Christov theory and double stratifications. The governing PDE models are altered into ODE models. These models are numerically solved by MATLAB bvp4c and analytically solved by the homotopy analysis method. The impact of governing flow parameters on fluid velocity, fluid temperature, fluid concentration, skin-friction coefficient, local Nusselt number, and local Sherwood number is scrutinized via graphs and tables. We acknowledged that the speed of the fluid becomes diminishes for more presence of porosity parameter. Also, we noted that the thermal and solutal boundary layer thicknesses are waning due to their corresponding stratification parameters. In addition, the maximum decreasing percentage of skin friction is obtained when the suction/injection parameter varies from 0.0 to 0.4 for Williamson and viscous fluids. The maximum increasing percentage of local Nusselt number occurs when the suction/injection parameter varies from 0.4 to 0.8 for Williamson and viscous fluids.

scholarly journals Numerical and Computer Simulations of Cross-Flow in the Streamwise Direction through a Moving Surface Comprising the Significant Impacts of Viscous Dissipation and Magnetic Fields: Stability Analysis and Dual Solutions

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yu-Ming Chu ◽  
Umair Khan ◽  
A. Zaib ◽  
S. H. A. M. Shah ◽  
Marin Marin
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Cross Flow ◽  
Dual Solutions ◽  
Lower Branch ◽  
Suction Parameter ◽  
Highly Nonlinear ◽  
Branch Solution ◽  
Flow Through ◽  
The Impact

The inspiration for this study is to explore the crucial impact of viscous dissipation (VISD) on magneto flow through a cross or secondary flow (CRF) in the way of streamwise. Utilizing the pertinent similarity method, the primary partial differential equations (PDEs) are changed into a highly nonlinear dimensional form of ordinary differential equations (ODEs). These dimensionless forms of ODEs are executed numerically by the aid of bvp4c solver. The impact of pertinent parameters such as the suction parameter, magnetic parameter, moving parameter, and viscous dissipation parameter is discussed with the help of plots. Dual solutions are obtained for certain values of a moving parameter. The velocities in the direction of streamwise, as well as cross-flow, decline in the upper branch solution, while the contrary impact is seen in the lower branch solution. However, the influence of suction on the velocities in both directions uplifts in the upper branch solution and shrinks in the lower branch solution. The analysis is also performed in terms of stability to inspect which solution is stable or unstable, and it is observed that the lower branch solution is unstable, whereas the upper branch one is stable.

scholarly journals Impact of Activation Energy in Darcy-Forchheimer Flow of Cross Nanofluid over a Radial Stretching Surface with Viscous Dissipation and Joule Heating

2021 ◽  
Vol 39 (5) ◽  
pp. 1557-1566
Author(s):  
Cherlacola Srinivas Reddy ◽  
Besthapu Prabhakar
Keyword(s):  
Activation Energy ◽  
Temperature Field ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Graphical Representation ◽  
Energy Parameter ◽  
System Of Nonlinear Equations ◽  
The Impact ◽  
Forchheimer Flow

This framework analyzes the impact of activation energy (AE) and binary chemical reaction (BCR) in Darcy-Forchheimer flow of cross fluid with nanoparticles due to radially stretched surface. Moreover slip, joule heating and viscous dissipation aspects have been considered. Ordinary differential equations acquired from the modelled governing partial differential equations with the assistance of suitable transformations. Further the system of nonlinear equations is computed numerically by Runge-Kutta-Fehlberg method cum shooting technique. Graphical representation has been given to analyze the velocity, temperature and concentration fields with the effect of various pertinent parameters. It is evident that inertia coefficient declines the velocity. Velocity decays for larger Weissenberg number while opposite trend observed in temperature field. Temperature field rises for augmented values of Eckert number. Concentration increases with increase of energy parameter.

scholarly journals Mathematical analysis of the flow and heat transfer of Ag-Cu hybrid nanofluid over a stretching/shrinking surface with convective boundary condition and viscous dissipation

2020 ◽  
Vol 1 (01) ◽  
pp. 11-22
Author(s):  
R. Jusoh ◽  
K. Naganthran ◽  
A. Jamaludin ◽  
M.H. Ariff ◽  
M.F.M. Basir ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Biot Number ◽  
Convective Boundary Condition ◽  
Hybrid Nanofluid ◽  
Convective Boundary ◽  
Nanoparticles Concentration ◽  
The Impact

Hybrid nanofluid has a vast potential of applications in the cooling system due to the high thermal conductivity. This study emphasizes on the impact of the convective boundary condition and viscous dissipation to the heat transfer of Ag-Cu hybrid nanofluid. A suitable similarity transformation is used to transform the partial differential equations of mass, momentum and energy into the ordinary differential equations. A finite difference code known as bvp4c in Matlab is employed to generate the numerical solutions. Stability analysis is conducted since dual solutions are generated in this study and the first solution exhibits the stability properties. The influence of variations in the suction parameter, viscous dissipation, nanoparticles concentration and Biot number on the on the temperature and velocity profiles of the hybrid nanofluid are portrayed. The rate of heat transfer is prominently higher with the augmentation of the Biot number and Ag nanoparticles concentration.

scholarly journals Approximate Analytical Analysis of Unsteady MHD Mixed Flow of Non-Newtonian Hybrid Nanofluid over a Stretching Surface

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 138
Author(s):  
Ali Rehman ◽  
Zabidin Salleh
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Base Fluid ◽  
Research Work ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Optimal Homotopy Analysis Method ◽  
Analytical Analysis ◽  
Transfer Ratio ◽  
The Impact

This paper analyses the two-dimensional unsteady and incompressible flow of a non-Newtonian hybrid nanofluid over a stretching surface. The nanofluid formulated in the present study is TiO2 + Ag + blood, and TiO2 + blood, where in this combination TiO2 + blood is the base fluid and TiO2 + Ag + blood represents the hybrid nanofluid. The aim of the present research work is to improve the heat transfer ratio because the heat transfer ratio of the hybrid nanofluid is higher than that of the base fluid. The novelty of the recent work is the approximate analytical analysis of the magnetohydrodynamics mixed non-Newtonian hybrid nanofluid over a stretching surface. This type of combination, where TiO2+blood is the base fluid and TiO2 + Ag + blood is the hybrid nanofluid, is studied for the first time in the literature. The fundamental partial differential equations are transformed to a set of nonlinear ordinary differential equations with the guide of some appropriate similarity transformations. The analytical approximate method, namely the optimal homotopy analysis method (OHAM), is used for the approximate analytical solution. The convergence of the OHAM for particular problems is also discussed. The impact of the magnetic parameter, dynamic viscosity parameter, stretching surface parameter and Prandtl number is interpreted through graphs. The skin friction coefficient and Nusselt number are explained in table form. The present work is found to be in very good agreement with those published earlier.

Influence of rotating magnetic field on Maxwell saturated ferrofluid flow over a heated stretching sheet with heat generation/absorption

2019 ◽  
Vol 20 (5) ◽  
pp. 502 ◽  
Author(s):  
Aaqib Majeed ◽  
Ahmed Zeeshan ◽  
Farzan Majeed Noori ◽  
Usman Masud
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
Velocity Field ◽  
Differential Equations ◽  
Heat Transport ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
The Impact

This article is focused on Maxwell ferromagnetic fluid and heat transport characteristics under the impact of magnetic field generated due to dipole field. The viscous dissipation and heat generation/absorption are also taken into account. Flow here is instigated by linearly stretchable surface, which is assumed to be permeable. Also description of magneto-thermo-mechanical (ferrohydrodynamic) interaction elaborates the fluid motion as compared to hydrodynamic case. Problem is modeled using continuity, momentum and heat transport equation. To implement the numerical procedure, firstly we transform the partial differential equations (PDEs) into ordinary differential equations (ODEs) by applying similarity approach, secondly resulting boundary value problem (BVP) is transformed into an initial value problem (IVP). Then resulting set of non-linear differentials equations is solved computationally with the aid of Runge–Kutta scheme with shooting algorithm using MATLAB. The flow situation is carried out by considering the influence of pertinent parameters namely ferro-hydrodynamic interaction parameter, Maxwell parameter, suction/injection and viscous dissipation on flow velocity field, temperature field, friction factor and heat transfer rate are deliberated via graphs. The present numerical values are associated with those available previously in the open literature for Newtonian fluid case (γ 1 = 0) to check the validity of the solution. It is inferred that interaction of magneto-thermo-mechanical is to slow down the fluid motion. We also witnessed that by considering the Maxwell and ferrohydrodynamic parameter there is decrement in velocity field whereas opposite behavior is noted for temperature field.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

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